441 KB0 KB179 KB2025Imrich, WilfriedKlep, IgorSmertnig, Danielštevilka:1, article p1.1118 str.letnik:8DOI:10.26493/2590-9770.1816.e85COBISSID_HOST:234550019ISSN:2590-9770URN:URN:NBN:SI:doc-VPH7KPFJenFakulteta za matematiko, naravoslovje in informacijske tehnologijeThe art of discrete and applied mathematicscancellation propertygraph productsmonoid algebraspower series ringsuniqueness of rootsMonoid algebras and graph products|In this note, we extend results about unique ?$n^{\rm th}$? roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic product. We show that these results also hold for graphs with countably many finite connected components, as long as every connected component appears only finitely often (up to isomorphism). The proofs are via monoid algebras and generalized power series ringsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije